Robert James Purkiss, 38, was remanded in custody by a judge after being arrested on Thursday, Britain's National Crime Agency said in a statement.

Purkiss is wanted in Kenya on suspicion of killing 21-year-old Agnes Wanjiru in 2012, in a case that has caused diplomatic tensions between the two countries.

The body of the young mother was found in a septic tank two months after she reportedly went partying with British soldiers at a hotel in Nanyuki, a town in central Kenya where Britain has a permanent army garrison.

In September, a Nairobi High Court judge issued an arrest warrant for Purkiss, with local prosecutors saying extradition proceedings would be initiated to bring him before a Kenyan court.

Purkiss, a married father of two, told Westminster Magistrates' Court in London that he did not consent to being extradited, the Press Association news agency reported.

Judge Briony Clarke rejected his application for bail and ordered him to appear before the court again on November 14.

Earlier, Joel Smith, a lawyer acting for Britain's interior ministry, laid out the case against Purkiss.

He told the court that Wanjiru was last seen alive on the night of March 31, 2012 when she left a hotel in Nanyuki with a soldier.

She was reported missing on April 2 and her body was found "significantly decomposed" on June 5.

Smith said a post-mortem examination identified a stab wound to the lower abdomen and a collapsed lung.

He told the court that colleagues of the accused had told military police in Kenya that Purkiss had confessed to killing Wanjiru and even joked about her death in Facebook messages.

Purkiss's lawyer David Josse said that his client "vehemently denies" murder and that he has received funding from Britain's defence ministry to pay for his defence.

The case was a source of contention between Kenyan authorities and Britain's previous Conservative government, and was in limbo for years.

The Labour party, which ousted the Conservatives from power in July last year, has vowed to support the Kenyan investigation and "secure a resolution to this case".

Since Kenya gained independence in 1963, Britain has kept a permanent army base near Nanyuki, around 200 kilometres (125 miles) north of the capital Nairobi.

The British Army Training Unit in Kenya is an economic lifeline for many in Nanyuki but has faced criticism over allegations of misconduct by its soldiers, as well as the maiming of civilians by unexploded ordnance.